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Second-order reaction is a type of chemical reaction wherein the concentrations of one second-order reactant or two first order reactants determine the outcome. The reaction occurs at a rate that is proportional to the square of the concentration of a reactant, or the product of the concentrations of two reactants. The rate equation of a second order reaction is given by,
r = k[A].[B]y
Second-order reaction chemical kinetics can be used to describe many important biological reactions, such as the formation of double-stranded DNA from two complementary strands. The reaction rate refers to how fast the reactants are consumed.
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Key Terms: Second order Reaction, rate of reaction, reactants, power rule of integration, Second-order kinetics, Rate equation, Chemical kinetics, reaction rate
What is Second-Order Reaction?
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Second-order reaction is a chemical reaction in which the concentrations of a one-second order reactant or two first order reactants determine the outcome of the reaction. The order of a chemical reaction is defined as the sum of the powers of the concentrations of the reactants in the rate law statement. The concentration of the reactants determines whether the reaction is first order, second-order, or pseudo-first-order reaction.
The rate of a second-order reaction is given by:
| r = k[A].[B]y |
When the total of x and y (which corresponds to the order of the chemical reaction in question) equals two, the chemical reaction is said to be a second order reaction.
Order of reaction
Also Read:
| Related Articles | ||
|---|---|---|
| Integrated Rate Equations | Rate of Chemical Reaction | Inversion Chemical Reaction |
| Order of Reactions | Collision Theory of Chemical Reactions | Zero Order Reaction |
Second Order Chemical Reaction Examples
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Some of the second order chemical reactions are unbalanced. This is due to the fact that some reactions are intermediates in other processes.
H+ + OH- → H2O
Water is made up of hydrogen ions and hydroxyl ions.
2NO2 → 2NO + O2
Nitrogen dioxide is broken down into nitrogen monoxide and oxygen.
2 HI → I2 + H2
Hydrogen Iodide breaks down into two gases: iodine and hydrogen.
O + O3 → O2 + O2
Oxygen molecules are formed when oxygen atoms and ozone combine during burning.
Rate of Second-Order Reaction
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For a reaction,
aA + bB → cC + dD
the second-order reaction rate in terms of the reactant concentrations can be expressed as,
k [A].[B] y = rate
Here,
k → Constant
[A] and [B] → Reactant concentrations
x and y → Experimentally determined reaction orders, which are not to be confused with the stoichiometric coefficients a and b.
- The sum of the variables x and y determines the order of a chemical reaction.
- A reaction of second order is one in which x + y = 2.
- This can happen if one reactant is used at a rate proportional to its concentration squared (rate = k[A]2), or if both reactants are consumed linearly over time (rate = k[A][B]).
- The rate constant, k, of a second-order process is measured in M-1s-1.
Second-order reactions usually have the following form:
2 A → products or A + B → products
Second-Order Reactions' Differential & Integrated Rate Equation
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The differential rate law equation can be expressed as follows in the case of one-second order reactant forming a particular product in a chemical reaction:
−d[A] / dt = k[A]2
This differential form must be rearranged as follows to obtain the integrated rate equation.
| d[A]/[A]2 = −kdt |
The following equation is obtained by integrating on both sides and taking into account the change in reactant concentration between time 0 and time t.
Applying the power rule of integration, the equation changes to:
∫dx /x2 = −1/x + C
Where
C → Integration Constant.
The following equation can now be obtained by applying the power rule to the previous equation.
1 / [R]t – 1/[R]0 = kt
And this is the final required integrated rate of the equation of the second-order reaction.
Second Order Reaction Graph
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The following reaction is generated by rearranging the integrated rate law equation of reactions of the second-order and generalising [R]t as [R].
1/[R] = kt + 1/[R]0
Plotting a straight line (y=mx + c) corresponding to this equation (y = 1/[R] , x = t , m = k , c = 1/[R]0)
Second Order Reaction Graph
The slope of the straight line equals the value of the rate constant, k.
Things to Remember
- A second-order reaction is a type of chemical reaction in which the concentrations of one second-order reactant or two first order reactants determine the outcome.
- Second-order kinetics can be used to describe many important biological reactions, such as the formation of double-stranded DNA from two complementary strands.
- The sum of the exponents in the rate law equals two in a second-order reaction.
- Rate Equation of second-order reactions: r = k[A]x[B]y
- The differential rate law equation of a second-order reaction: −d[R] /dt = k[R]2
- The Integrated rate law equation of a second-order reaction: 1/[R]t – 1/[R]0 = kt
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Sample Questions
Ques. What is the second-order rate law? (2 marks)
Ans. A second-order reaction is a type of chemical reaction in which the concentrations of one second-order reactant or two first order reactants determine the outcome. Second-order kinetics can be used to describe many important biological reactions, such as the formation of double-stranded DNA from two complementary strands. The sum of the exponents in the rate law is equal to two in a second-order reaction. It is expressed as r = k[A]x[B]y.
Ques. What is the order of the reaction whose rate constant has the same units as the rate of reaction?
(ii) For a reaction A + H2O → B; Rate ∝ [A],
What is the order of this reaction? (CBSE 2017) (2 marks)
Ans. (i) The reaction whose rate constant has the same units as the rate of reaction, will have zero-order of reaction.
(ii) The reaction A + H2O → B Rate ∝ [A]
The order of this reaction will be a pseudo-first-order reaction as the rate of reaction depends only on the concentration of A only.
Ques. How can you tell if a graph is of the first or second order? (2 marks)
Ans. Draw a graph of the inverse of concentration 'A' versus 'time'. If the outcome is a straight line with a negative slope, the function is of the first order. But if a positive straight line shows up with a positive slope, the function is of second order.
Ques. What is the second-order integrated rate law? (2 marks)
Ans. The Integrated rate law equation of a second-order reaction: 1/[R]t – 1/[R]0 = kt
Ques. Define the rate of a reaction. (CBSE 2010) (2 marks)
Ans. Rate of a reaction: Either, The change in the concentration of any one of the reactants or products per unit of time is called the rate of a reaction. Or, The rate of a chemical reaction is the change in the molar concentration of the species taking part in a reaction per unit of time.
Ques. What are the units of k for a second-order reaction? (2 marks)
Ans. The unit of the second-order rate constant is M-1 s-1
Ques. Define the ‘activation energy’ of a reaction. (CBSE 2011) (2 marks)
Ans. The minimum extra amount of energy absorbed by the reactant molecules to form the activated complex is called activation energy.
The activation energy of the reaction decreases with the use of a catalyst.
Ques. If the reactant concentration changes from 0.08M to 0.04M in 10 minutes for the second-order reaction. Calculate the time it takes for the reactant concentration to reach 0.01M. (3 marks)
Ans. By substituting values given in data in the below equation,
1/[A]t − 1- 1/[A]0 = kt
We can find the rate constant k.
1/0.08 − 1/0.04 = k.10
K = 1.25
Using the same equation, we can calculate the time when the concentration of the reactant reaches 0.01M,
1/0.08 − 1/0.01 = 1.25t
t = 70 mins
As a result, the time it takes for the reactant concentration to reach 0.01M is 70 minutes.
Ques. A reaction is of second order with respect to a reactant. How will the rate of reaction be affected if the concentration of this reactant is
(i) doubled, (ii) reduced to half? (Delhi 2009)
For second order reaction Let [A] = a then Rate = Ka2
(i) If [A] = 2a then Rate = K (2a)2 = 4 Ka2
∴ The rate of reaction becomes 4 times
(ii) If [A] = a/2 then Rate = K (a/2)2=Ka2/4
∴ The rate of reaction will be 1/4th.
Ques. Distinguish between the ‘rate expression’ and ‘rate constant’ of a reaction. (CBSE 2011) (2 marks)
Ans. Rate expression: The expression which expresses the rate of reaction in terms of molar concentrations of the reactants with each term raised to their power, which may or may not be the same as the stoichiometric coefficient of that reactant in the balanced chemical equation.
The rate constant: The rate of reaction when the molar concentration of each reactant is taken as unity.
Ques. What do you understand by the rate law and rate constant of a reaction? Identify the order of a reaction if the units of its rate constant are : (i) L-1 mol s-1 (ii) L mol-1 s-1 (CBSE 2011) (2 marks)
Ans. The rate of reaction is found to depend on the α concentration of term of reactant A and β concentration term of reactant B
Then Rate of reaction ∝ [A]α [B]β
or Rate = K [A]α [B]β
This expression is called Rate law.
‘K’ in this expression is called the Rate constant. Rate constant’s unit :
(i) Unit = L-1 mol s-1 → Zero order reaction
(ii) Unit = L mol-1 s-1 → Second order reaction.
Ques. A reaction is of second order with respect to a reactant. How is its rate affected if the concentration of the reactant is (i) doubled or (ii) reduced to half? (CBSE 2012) (2 marks)
Ans. As Formula, r = K[R|2 …(Given)
(i) R’ = 2R ⇒ r = K[2R]-1 = 4KR-1
∴ The rate becomes 4 times than original rate
Ques. Write two differences between ‘order of reaction’ and ‘molecularity of reaction’. (CBSE 2014) (2 marks)
Ans.
| Order of reaction | Molecularity of reaction |
|---|---|
| (i) It is the sum of tire concentration terms on which the rate of reaction actually depends. | It is the number of atoms, ions or molecules that must collide with one another simultaneously so as to result in a chemical reaction. |
| (ii) It can be fractional as well as zero. | it is always a whole number. |
Ques. Explain the following terms :
(i) Rate constant (k)
(ii) Half-life period of a reaction (t1/2) (CBSE 2014) (2 marks)
Ans. (i) Rate constant (k): It is a proportionality constant and is equal to the rate of reaction when the molar concentration of each of the reactants is unity.
(ii) Half-life period of a reaction (t1/2): The time taken for half of the reaction to complete is called the half-life period.(R)t.
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